Results 171 to 180 of about 13,897 (205)

DEGENERATE BIFURCATIONS OF HETERODIMENSIONAL CYCLES WITH ORBIT FLIP

International Journal of Bifurcation and Chaos, 2013
In this paper, nongeneric bifurcation analysis near heterodimensional cycles with orbit flip is investigated for three-dimensional systems. With the aid of a suitable local coordinate system, the Poincaré map is constructed. By means of the bifurcation equations, the existence, nonexistence, coexistence and uniqueness of homoclinic orbit, periodic ...
Liu, Xingbo, Liu, Junying, Zhu, Deming
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Degenerate Orbit Flip Homoclinic Bifurcations with Higher Dimensions

Acta Mathematica Sinica, English Series, 2006
For higher dimensional systems, bifurcations of a degenerate homoclinic orbit with orbit flip are studied. By establishing local coordinates near the homoclinic orbit, conditions are given sufficient for the existence and uniqueness of a 1-homoclinic orbit and a 1-periodic orbit.
Wu, Ran Chao, Sun, Jian Hua
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Heterodimensional cycle bifurcation with two orbit flips

Nonlinear Dynamics, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Xingbo, Xu, Yancong, Wang, Sisi
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Flip bifurcations of two systems of difference equations

Mathematical Methods in the Applied Sciences, 2020
This paper investigates the bifurcations of the following difference equations where a,b,c, and d are positive constants and the initial conditions x0 and y0 are positive numbers. Psarros, Papaschinopoulos, and Schinas (Math. Methods Appl. Sci., 2016, 39: 5216–5222) presented the semistability of the fixed point (0,0) when one eigenvalue is equal to ...
Qi Cheng, Shengfu Deng
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Homoclinic flip bifurcations accompanied by transcritical bifurcation

Chinese Annals of Mathematics, Series B, 2011
The author investigates the bifurcation of a homoclinic loop with a nonhyperbolic equilibrium by constructing a suitable Poincaré map. Using the fundamental solutions to linear variational equations as an active coordinate system, he constructs a global map which is composed of a regular map in the tubular neighborhood of the homoclinic orbit and a ...
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Homoclinic Bifurcation of Orbit Flip with Resonant Principal Eigenvalues

Acta Mathematica Sinica, English Series, 2005
The authors consider the general 4-dimensional system in a resonant orbit flip situation. The resonance takes place between the two principal eigenvalues. This is a kind of codimension-3 bifurcation. The authors obtain the existence, number, coexistence of the 1-homoclinic orbit, 1-periodic orbit and 2-homoclinic orbit, etc.
Zhang, Tiansi, Zhu, Deming
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NONRESONANT BIFURCATIONS OF HETEROCLINIC LOOPS WITH ONE INCLINATION FLIP

International Journal of Bifurcation and Chaos, 2011
Heteroclinic bifurcations in four-dimensional vector fields are investigated by setting up local coordinates near a heteroclinic loop. This heteroclinic loop consists of two principal heteroclinic orbits, but there is one stable foliation that involves an inclination flip.
Shui, Shuliang, Li, Jingjing, Zhang, Xuyang   +2 more
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Bifurcations of heterodimensional cycles with one orbit flip and one inclination flip

Nonlinear Dynamics, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xu, Yancong, Zhu, Deming
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An equivariant, inclination-flip, heteroclinic bifurcation

Nonlinearity, 1996
Summary: We examine a heteroclinic bifurcation occurring in families of equivariant vector fields. Within these families, the flows contain structurally stable heteroclinic cycles. The flow can twist around the cycle to produce what is the equivalent of an `inclination-flip' homoclinic orbit.
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Flip bifurcation and Neimark–Sacker bifurcation in a discrete predator–prey model with harvesting

International Journal of Biomathematics, 2019
In this paper, a difference-algebraic predator–prey model is proposed, and its complex dynamical behaviors are analyzed. The model is a discrete singular system, which is obtained by using Euler scheme to discretize a differential-algebraic predator–prey model with harvesting that we establish.
Wei Liu, Yaolin Jiang
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